A microwave filter is an electromagnetic circuit that can be tuned to pass energy at a specified resonant frequency. Accordingly, microwave filters are commonly used in telecommunication applications to transmit energy in a desired band of frequencies (i.e. the passband) and reject energy at unwanted frequencies (i.e. the stopband) that are outside of the desired band. In addition, the microwave filter should preferably meet some performance criteria for properties which typically include insertion loss (i.e. the minimum loss in the passband), loss variation (i.e. the flatness of the insertion loss in the passband), rejection or isolation (the attenuation in the stopband), group delay (i.e. related to the phase characteristics of the filter) and return loss.
In order to design a microwave filter to meet the above-mentioned performance criteria, it is well known in the art to vary the shape of the transfer function of the microwave filter. The transfer function (H(s)) of the microwave filter can be defined by a polynomial according to equation 1 shown below.                               H          ⁡                      (            s            )                          =                              D            ⁡                          (              s              )                                            E            ⁡                          (              s              )                                                          (        1        )            where D(s) and E(s) are polynomials of the variable s, s=jω, j=√{square root over (−1)} and ω is angular frequency. The roots of the numerator polynomial D(s) are known as transmission zeros of the filter and the roots of the denominator polynomial E(s) are known as poles of the filter. The shape of the transfer function (H(s)) can be changed to meet the performance criteria by varying the number of transmission zeros and poles and using different filter types such as Chebychev, elliptical, Butterworth, etc. to obtain different placements for the locations of these transmission zeros and poles.
By varying the number of poles (i.e. the order of the filter), the physical characteristics of the microwave filter such as the size and shape will change. In addition to varying the number of poles, the shape, size, quality and conductivity of the internal resonators of the filter may also be changed. As is well known to those skilled in the art, a resonator may be a hollow metallic chamber with precise dimensions. The chamber, also referred to as a cavity, usually incorporates relatively small apertures (i.e. irises) to couple energy between at least one other chamber. Alternatively, resonators may be in the form of a cavity having a metallic post or ceramic dielectric material. The dimensions of the resonators are determined by the use of design and synthesis tools as is well known to those skilled in the art.
When the material type and the size of the resonators for the filter are chosen, the Q (i.e. quality) factor for the filter is set. The Q factor has a direct effect on the amount of insertion loss and pass-band flatness of the realized microwave filter. In particular, a filter having a higher Q factor will have lower insertion loss and sharper slopes (i.e. a more “square” filter shape) in the transition region between the passband and the stopband. In contrast, filters which have a low Q factor have a larger amount of energy dissipation due to larger insertion loss and will also exhibit a larger degradation in band edge sharpness. Examples of high Q factor filters include waveguide and dielectric resonator filters which have Q factors on the order of 8,000 to 15,000. An example of a low Q factor filter is a coaxial resonator filter which typically has a Q factor on the order of 2,000 to 5,000.
As is conventionally known, in order to increase the Q factor of the filter, and hence the performance of the filter, the size of the resonators must be increased which results in a larger and heavier filter. This is disadvantageous since multi-cavity microwave filters are typically used in various space craft communication systems such as communication satellites in which there are stringent restrictions on payload mass.
Another issue with microwave filter design is that the transfer function of a microwave filter represents an ideal filter with an infinite Q factor. Since a microwave filter cannot be realized (i.e. constructed) with an infinite Q factor, but rather with resonators having a finite Q factor, the performance of a realized microwave filter is not the same as the ideal filter. Accordingly, the transfer function of the realized microwave filter will have passband edges that slump downward which causes distortion and intermodulation. There is also degradation in the loss variation in the passband of the realized filter.
In order to improve the loss variation and band edge sharpness of a realized microwave filter, an approach using predistortion was proposed by Livingston (Livingston, R. M., “Predistorted Waveguide filters”, G-MTT Int. Microwave Symp., Dig. 1969, pp 291-297) and Williams et al. (Williams, A. E., Bush, W. G. and Bonetti R. R., “Predistortion Technique for Multicoupled Resonator Filters”, IEEE Transactions on Microwave Theory and Techniques, Vol. MTT-33, No. 5, May 1985, pp 402-407). Livingston and Williams taught that predistortion of the poles could be used to correct for the effects of energy dissipation in the realized microwave filter to make the response of the realized filter approach that of an ideal filter. In particular, Livingston and Williams applied predistortion to the poles of a microwave filter having a high Q factor of 8,000. The poles of the filter transfer function were each predistorted by shifting the real part of the poles towards the jw axis by a similar amount before the filter was realized. The result was that the loss variation and band-edge sharpness of the realized predistorted filter were improved. However, the insertion loss and return loss degradation of the realized predistorted filter were severe to the point that the realized predistorted filter could not be used in a practical application. Furthermore, the realized predistorted filter had an undesirable increase in group delay ripple because the predistorted method did not consider group delay compensation.